Satellite image deconvolution
using complex wavelet packets

André Jalobeanu - Laure Blanc-Féraud - Josiane Zerubia
See the Demo (PDF)

The deconvolution of blurred and noisy satellite images is an ill-posed inverse problem. The direct inversion leads to unacceptable noise amplification. Usually, either the problem is regularized during the inversion process, or the noise is filtered after deconvolution and decomposition in the wavelet transform domain. Herein, we have developed the second solution, by thresholding the coefficients of a new complex wavelet packet transform; the thresholding functions are automatically estimated. The use of complex wavelet packets enables translation invariance, and takes into account the directions, while remaining of complexity O(N).

The obtained results exhibit both correctly restored textures and a high SNR in homogeneous areas. Compared to concurrent algorithms, the proposed method is faster, rotation invariant and takes into account the directions of the details and textures of the image to restore them better.

The images deconvolved this way can be used as they are (the restoration step proposed here can be directly inserted in the acquisition chain). But they also can provide a starting point of an adaptive regularization method, enabling one to obtain sharper edges.